In mathamatics and, computer programming the Order of Operations (sometimes called Operator Precedence) is a rule used to clarify unambiguously which procedures should be performed first in a given mathematical expressions.
For example, in mathematics and most computer languages multiplication is done before addition; in the expression 2 + 3 × 4, the answer is 14. Brackets, "( and ), { and }, or [ and ]", which have their own rules, may be used to avoid confusion, thus the preceding expression may also be rendered 2 + (3 × 4), but the brackets are unnecessary as multiplication still has precedence without them.
From the introduction of modern algebraic notation, where juxtaposition indicates multiplication of variables, multiplication took precedence over addition, whichever side of a number it appeared on. Thus 3 + 4 × 5 = 4 × 5 + 3 = 23. When exponents were first introduced, in the 16th and 17th centuries, exponents took precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base. Thus 3 + 52 = 28 and 3 × 52 = 75. To change the order of operations. (an overline or underline) was used. Today, brackets are used to explicitly denote precedence by grouping parts of an expression that should be evaluated first. Thus, to force addition to precede multiplication, we write (2 + 3) × 4 = 20, and to force addition to precede exponentiation, we write (3 + 5)2 = 64. for more information:
Easy Problem: Simplify all operations inside parentheses is what you do?Answer: yes
Easy Problem: 4 + 32 = 4 + 9 = ?Answer: 13
Hard Problem: 4 + 2×3 = (4 + 2)×3 = 6×3= ?Answer: 18
Hard Problem: 4 + 2×3 = 4 + (2×3) = 4 + 6 = ?Answer: 10
Order of operations
From Wikipedia, the free encyclopediaIn mathamatics and, computer programming the Order of Operations (sometimes called Operator Precedence) is a rule used to clarify unambiguously which procedures should be performed first in a given mathematical expressions.
For example, in mathematics and most computer languages multiplication is done before addition; in the expression 2 + 3 × 4, the answer is 14. Brackets, "( and ), { and }, or [ and ]", which have their own rules, may be used to avoid confusion, thus the preceding expression may also be rendered 2 + (3 × 4), but the brackets are unnecessary as multiplication still has precedence without them.
From the introduction of modern algebraic notation, where juxtaposition indicates multiplication of variables, multiplication took precedence over addition, whichever side of a number it appeared on. Thus 3 + 4 × 5 = 4 × 5 + 3 = 23. When exponents were first introduced, in the 16th and 17th centuries, exponents took precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base. Thus 3 + 52 = 28 and 3 × 52 = 75. To change the order of operations. (an overline or underline) was used. Today, brackets are used to explicitly denote precedence by grouping parts of an expression that should be evaluated first. Thus, to force addition to precede multiplication, we write (2 + 3) × 4 = 20, and to force addition to precede exponentiation, we write (3 + 5)2 = 64.
for more information:
Easy Problem: Simplify all operations inside parentheses is what you do?Answer: yes
Easy Problem: 4 + 32 = 4 + 9 = ?Answer: 13
Hard Problem: 4 + 2×3 = (4 + 2)×3 = 6×3= ?Answer: 18
Hard Problem: 4 + 2×3 = 4 + (2×3) = 4 + 6 = ?Answer: 10